Am 18.09.21 um 04:56 schrieb Michael Turner:
Or, you can tell them, "Just learn lambda calculus, then study monads algebraically, and here's a side dish of category theory while I'm it. Bon appetit." How's that working for you, guys? It doesn't work for me. And I don't think it's because I can't do the math. It's that I often write code to see whether I'm thinking about a problem the right way.
Same here.
I'm no star hacker, but "workflow" feels like it will make my fingertips smarter. "Programmable semicolon" feels like it will make my fingertips smarter. You think top-down mathematically?
I'd venture that most mathematicians don't use such a purely formal top-down approach when thinking about a problem. Intuition about concepts is very important. Mathematical writing often gives the wrong impression that in order to understand a new concept, you just have to read the formal definition and then make logical deductions. This is not how it works in practice and those who are honest will readily admit that. You need to study concrete examples, and you need to work through exercises to develop true understanding. As for monads, even though I do like the "overloaded semicolon" metaphor, the crucial point is not the sequencing as such, but rather how to express capturing and referencing intermediate results *in a statically typed fashion*. Cheers Ben -- I would rather have questions that cannot be answered, than answers that cannot be questioned. -- Richard Feynman